| .file "sincosf.s" |
| |
| |
| // Copyright (c) 2000 - 2005, Intel Corporation |
| // All rights reserved. |
| // |
| // Contributed 2000 by the Intel Numerics Group, Intel Corporation |
| // |
| // Redistribution and use in source and binary forms, with or without |
| // modification, are permitted provided that the following conditions are |
| // met: |
| // |
| // * Redistributions of source code must retain the above copyright |
| // notice, this list of conditions and the following disclaimer. |
| // |
| // * Redistributions in binary form must reproduce the above copyright |
| // notice, this list of conditions and the following disclaimer in the |
| // documentation and/or other materials provided with the distribution. |
| // |
| // * The name of Intel Corporation may not be used to endorse or promote |
| // products derived from this software without specific prior written |
| // permission. |
| |
| // THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS |
| // "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT |
| // LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR |
| // A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL INTEL OR ITS |
| // CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, |
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| // PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR |
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| // OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY OR TORT (INCLUDING |
| // NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS |
| // SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. |
| // |
| // Intel Corporation is the author of this code, and requests that all |
| // problem reports or change requests be submitted to it directly at |
| // http://www.intel.com/software/products/opensource/libraries/num.htm. |
| // |
| // History |
| //============================================================== |
| // 02/02/00 Initial version |
| // 04/02/00 Unwind support added. |
| // 06/16/00 Updated tables to enforce symmetry |
| // 08/31/00 Saved 2 cycles in main path, and 9 in other paths. |
| // 09/20/00 The updated tables regressed to an old version, so reinstated them |
| // 10/18/00 Changed one table entry to ensure symmetry |
| // 01/03/01 Improved speed, fixed flag settings for small arguments. |
| // 02/18/02 Large arguments processing routine excluded |
| // 05/20/02 Cleaned up namespace and sf0 syntax |
| // 06/03/02 Insure inexact flag set for large arg result |
| // 09/05/02 Single precision version is made using double precision one as base |
| // 02/10/03 Reordered header: .section, .global, .proc, .align |
| // 03/31/05 Reformatted delimiters between data tables |
| // |
| // API |
| //============================================================== |
| // float sinf( float x); |
| // float cosf( float x); |
| // |
| // Overview of operation |
| //============================================================== |
| // |
| // Step 1 |
| // ====== |
| // Reduce x to region -1/2*pi/2^k ===== 0 ===== +1/2*pi/2^k where k=4 |
| // divide x by pi/2^k. |
| // Multiply by 2^k/pi. |
| // nfloat = Round result to integer (round-to-nearest) |
| // |
| // r = x - nfloat * pi/2^k |
| // Do this as (x - nfloat * HIGH(pi/2^k)) - nfloat * LOW(pi/2^k) |
| |
| // for increased accuracy. |
| // pi/2^k is stored as two numbers that when added make pi/2^k. |
| // pi/2^k = HIGH(pi/2^k) + LOW(pi/2^k) |
| // HIGH part is rounded to zero, LOW - to nearest |
| // |
| // x = (nfloat * pi/2^k) + r |
| // r is small enough that we can use a polynomial approximation |
| // and is referred to as the reduced argument. |
| // |
| // Step 3 |
| // ====== |
| // Take the unreduced part and remove the multiples of 2pi. |
| // So nfloat = nfloat (with lower k+1 bits cleared) + lower k+1 bits |
| // |
| // nfloat (with lower k+1 bits cleared) is a multiple of 2^(k+1) |
| // N * 2^(k+1) |
| // nfloat * pi/2^k = N * 2^(k+1) * pi/2^k + (lower k+1 bits) * pi/2^k |
| // nfloat * pi/2^k = N * 2 * pi + (lower k+1 bits) * pi/2^k |
| // nfloat * pi/2^k = N2pi + M * pi/2^k |
| // |
| // |
| // Sin(x) = Sin((nfloat * pi/2^k) + r) |
| // = Sin(nfloat * pi/2^k) * Cos(r) + Cos(nfloat * pi/2^k) * Sin(r) |
| // |
| // Sin(nfloat * pi/2^k) = Sin(N2pi + Mpi/2^k) |
| // = Sin(N2pi)Cos(Mpi/2^k) + Cos(N2pi)Sin(Mpi/2^k) |
| // = Sin(Mpi/2^k) |
| // |
| // Cos(nfloat * pi/2^k) = Cos(N2pi + Mpi/2^k) |
| // = Cos(N2pi)Cos(Mpi/2^k) + Sin(N2pi)Sin(Mpi/2^k) |
| // = Cos(Mpi/2^k) |
| // |
| // Sin(x) = Sin(Mpi/2^k) Cos(r) + Cos(Mpi/2^k) Sin(r) |
| // |
| // |
| // Step 4 |
| // ====== |
| // 0 <= M < 2^(k+1) |
| // There are 2^(k+1) Sin entries in a table. |
| // There are 2^(k+1) Cos entries in a table. |
| // |
| // Get Sin(Mpi/2^k) and Cos(Mpi/2^k) by table lookup. |
| // |
| // |
| // Step 5 |
| // ====== |
| // Calculate Cos(r) and Sin(r) by polynomial approximation. |
| // |
| // Cos(r) = 1 + r^2 q1 + r^4 q2 = Series for Cos |
| // Sin(r) = r + r^3 p1 + r^5 p2 = Series for Sin |
| // |
| // and the coefficients q1, q2 and p1, p2 are stored in a table |
| // |
| // |
| // Calculate |
| // Sin(x) = Sin(Mpi/2^k) Cos(r) + Cos(Mpi/2^k) Sin(r) |
| // |
| // as follows |
| // |
| // S[m] = Sin(Mpi/2^k) and C[m] = Cos(Mpi/2^k) |
| // rsq = r*r |
| // |
| // |
| // P = P1 + r^2*P2 |
| // Q = Q1 + r^2*Q2 |
| // |
| // rcub = r * rsq |
| // Sin(r) = r + rcub * P |
| // = r + r^3p1 + r^5p2 = Sin(r) |
| // |
| // The coefficients are not exactly these values, but almost. |
| // |
| // p1 = -1/6 = -1/3! |
| // p2 = 1/120 = 1/5! |
| // p3 = -1/5040 = -1/7! |
| // p4 = 1/362889 = 1/9! |
| // |
| // P = r + r^3 * P |
| // |
| // Answer = S[m] Cos(r) + C[m] P |
| // |
| // Cos(r) = 1 + rsq Q |
| // Cos(r) = 1 + r^2 Q |
| // Cos(r) = 1 + r^2 (q1 + r^2q2) |
| // Cos(r) = 1 + r^2q1 + r^4q2 |
| // |
| // S[m] Cos(r) = S[m](1 + rsq Q) |
| // S[m] Cos(r) = S[m] + S[m] rsq Q |
| // S[m] Cos(r) = S[m] + s_rsq Q |
| // Q = S[m] + s_rsq Q |
| // |
| // Then, |
| // |
| // Answer = Q + C[m] P |
| |
| |
| // Registers used |
| //============================================================== |
| // general input registers: |
| // r14 -> r19 |
| // r32 -> r45 |
| |
| // predicate registers used: |
| // p6 -> p14 |
| |
| // floating-point registers used |
| // f9 -> f15 |
| // f32 -> f61 |
| |
| // Assembly macros |
| //============================================================== |
| sincosf_NORM_f8 = f9 |
| sincosf_W = f10 |
| sincosf_int_Nfloat = f11 |
| sincosf_Nfloat = f12 |
| |
| sincosf_r = f13 |
| sincosf_rsq = f14 |
| sincosf_rcub = f15 |
| sincosf_save_tmp = f15 |
| |
| sincosf_Inv_Pi_by_16 = f32 |
| sincosf_Pi_by_16_1 = f33 |
| sincosf_Pi_by_16_2 = f34 |
| |
| sincosf_Inv_Pi_by_64 = f35 |
| |
| sincosf_Pi_by_16_3 = f36 |
| |
| sincosf_r_exact = f37 |
| |
| sincosf_Sm = f38 |
| sincosf_Cm = f39 |
| |
| sincosf_P1 = f40 |
| sincosf_Q1 = f41 |
| sincosf_P2 = f42 |
| sincosf_Q2 = f43 |
| sincosf_P3 = f44 |
| sincosf_Q3 = f45 |
| sincosf_P4 = f46 |
| sincosf_Q4 = f47 |
| |
| sincosf_P_temp1 = f48 |
| sincosf_P_temp2 = f49 |
| |
| sincosf_Q_temp1 = f50 |
| sincosf_Q_temp2 = f51 |
| |
| sincosf_P = f52 |
| sincosf_Q = f53 |
| |
| sincosf_srsq = f54 |
| |
| sincosf_SIG_INV_PI_BY_16_2TO61 = f55 |
| sincosf_RSHF_2TO61 = f56 |
| sincosf_RSHF = f57 |
| sincosf_2TOM61 = f58 |
| sincosf_NFLOAT = f59 |
| sincosf_W_2TO61_RSH = f60 |
| |
| fp_tmp = f61 |
| |
| ///////////////////////////////////////////////////////////// |
| |
| sincosf_AD_1 = r33 |
| sincosf_AD_2 = r34 |
| sincosf_exp_limit = r35 |
| sincosf_r_signexp = r36 |
| sincosf_AD_beta_table = r37 |
| sincosf_r_sincos = r38 |
| |
| sincosf_r_exp = r39 |
| sincosf_r_17_ones = r40 |
| |
| sincosf_GR_sig_inv_pi_by_16 = r14 |
| sincosf_GR_rshf_2to61 = r15 |
| sincosf_GR_rshf = r16 |
| sincosf_GR_exp_2tom61 = r17 |
| sincosf_GR_n = r18 |
| sincosf_GR_m = r19 |
| sincosf_GR_32m = r19 |
| sincosf_GR_all_ones = r19 |
| |
| gr_tmp = r41 |
| GR_SAVE_PFS = r41 |
| GR_SAVE_B0 = r42 |
| GR_SAVE_GP = r43 |
| |
| RODATA |
| .align 16 |
| |
| // Pi/16 parts |
| LOCAL_OBJECT_START(double_sincosf_pi) |
| data8 0xC90FDAA22168C234, 0x00003FFC // pi/16 1st part |
| data8 0xC4C6628B80DC1CD1, 0x00003FBC // pi/16 2nd part |
| LOCAL_OBJECT_END(double_sincosf_pi) |
| |
| // Coefficients for polynomials |
| LOCAL_OBJECT_START(double_sincosf_pq_k4) |
| data8 0x3F810FABB668E9A2 // P2 |
| data8 0x3FA552E3D6DE75C9 // Q2 |
| data8 0xBFC555554447BC7F // P1 |
| data8 0xBFDFFFFFC447610A // Q1 |
| LOCAL_OBJECT_END(double_sincosf_pq_k4) |
| |
| // Sincos table (S[m], C[m]) |
| LOCAL_OBJECT_START(double_sin_cos_beta_k4) |
| data8 0x0000000000000000 // sin ( 0 Pi / 16 ) |
| data8 0x3FF0000000000000 // cos ( 0 Pi / 16 ) |
| // |
| data8 0x3FC8F8B83C69A60B // sin ( 1 Pi / 16 ) |
| data8 0x3FEF6297CFF75CB0 // cos ( 1 Pi / 16 ) |
| // |
| data8 0x3FD87DE2A6AEA963 // sin ( 2 Pi / 16 ) |
| data8 0x3FED906BCF328D46 // cos ( 2 Pi / 16 ) |
| // |
| data8 0x3FE1C73B39AE68C8 // sin ( 3 Pi / 16 ) |
| data8 0x3FEA9B66290EA1A3 // cos ( 3 Pi / 16 ) |
| // |
| data8 0x3FE6A09E667F3BCD // sin ( 4 Pi / 16 ) |
| data8 0x3FE6A09E667F3BCD // cos ( 4 Pi / 16 ) |
| // |
| data8 0x3FEA9B66290EA1A3 // sin ( 5 Pi / 16 ) |
| data8 0x3FE1C73B39AE68C8 // cos ( 5 Pi / 16 ) |
| // |
| data8 0x3FED906BCF328D46 // sin ( 6 Pi / 16 ) |
| data8 0x3FD87DE2A6AEA963 // cos ( 6 Pi / 16 ) |
| // |
| data8 0x3FEF6297CFF75CB0 // sin ( 7 Pi / 16 ) |
| data8 0x3FC8F8B83C69A60B // cos ( 7 Pi / 16 ) |
| // |
| data8 0x3FF0000000000000 // sin ( 8 Pi / 16 ) |
| data8 0x0000000000000000 // cos ( 8 Pi / 16 ) |
| // |
| data8 0x3FEF6297CFF75CB0 // sin ( 9 Pi / 16 ) |
| data8 0xBFC8F8B83C69A60B // cos ( 9 Pi / 16 ) |
| // |
| data8 0x3FED906BCF328D46 // sin ( 10 Pi / 16 ) |
| data8 0xBFD87DE2A6AEA963 // cos ( 10 Pi / 16 ) |
| // |
| data8 0x3FEA9B66290EA1A3 // sin ( 11 Pi / 16 ) |
| data8 0xBFE1C73B39AE68C8 // cos ( 11 Pi / 16 ) |
| // |
| data8 0x3FE6A09E667F3BCD // sin ( 12 Pi / 16 ) |
| data8 0xBFE6A09E667F3BCD // cos ( 12 Pi / 16 ) |
| // |
| data8 0x3FE1C73B39AE68C8 // sin ( 13 Pi / 16 ) |
| data8 0xBFEA9B66290EA1A3 // cos ( 13 Pi / 16 ) |
| // |
| data8 0x3FD87DE2A6AEA963 // sin ( 14 Pi / 16 ) |
| data8 0xBFED906BCF328D46 // cos ( 14 Pi / 16 ) |
| // |
| data8 0x3FC8F8B83C69A60B // sin ( 15 Pi / 16 ) |
| data8 0xBFEF6297CFF75CB0 // cos ( 15 Pi / 16 ) |
| // |
| data8 0x0000000000000000 // sin ( 16 Pi / 16 ) |
| data8 0xBFF0000000000000 // cos ( 16 Pi / 16 ) |
| // |
| data8 0xBFC8F8B83C69A60B // sin ( 17 Pi / 16 ) |
| data8 0xBFEF6297CFF75CB0 // cos ( 17 Pi / 16 ) |
| // |
| data8 0xBFD87DE2A6AEA963 // sin ( 18 Pi / 16 ) |
| data8 0xBFED906BCF328D46 // cos ( 18 Pi / 16 ) |
| // |
| data8 0xBFE1C73B39AE68C8 // sin ( 19 Pi / 16 ) |
| data8 0xBFEA9B66290EA1A3 // cos ( 19 Pi / 16 ) |
| // |
| data8 0xBFE6A09E667F3BCD // sin ( 20 Pi / 16 ) |
| data8 0xBFE6A09E667F3BCD // cos ( 20 Pi / 16 ) |
| // |
| data8 0xBFEA9B66290EA1A3 // sin ( 21 Pi / 16 ) |
| data8 0xBFE1C73B39AE68C8 // cos ( 21 Pi / 16 ) |
| // |
| data8 0xBFED906BCF328D46 // sin ( 22 Pi / 16 ) |
| data8 0xBFD87DE2A6AEA963 // cos ( 22 Pi / 16 ) |
| // |
| data8 0xBFEF6297CFF75CB0 // sin ( 23 Pi / 16 ) |
| data8 0xBFC8F8B83C69A60B // cos ( 23 Pi / 16 ) |
| // |
| data8 0xBFF0000000000000 // sin ( 24 Pi / 16 ) |
| data8 0x0000000000000000 // cos ( 24 Pi / 16 ) |
| // |
| data8 0xBFEF6297CFF75CB0 // sin ( 25 Pi / 16 ) |
| data8 0x3FC8F8B83C69A60B // cos ( 25 Pi / 16 ) |
| // |
| data8 0xBFED906BCF328D46 // sin ( 26 Pi / 16 ) |
| data8 0x3FD87DE2A6AEA963 // cos ( 26 Pi / 16 ) |
| // |
| data8 0xBFEA9B66290EA1A3 // sin ( 27 Pi / 16 ) |
| data8 0x3FE1C73B39AE68C8 // cos ( 27 Pi / 16 ) |
| // |
| data8 0xBFE6A09E667F3BCD // sin ( 28 Pi / 16 ) |
| data8 0x3FE6A09E667F3BCD // cos ( 28 Pi / 16 ) |
| // |
| data8 0xBFE1C73B39AE68C8 // sin ( 29 Pi / 16 ) |
| data8 0x3FEA9B66290EA1A3 // cos ( 29 Pi / 16 ) |
| // |
| data8 0xBFD87DE2A6AEA963 // sin ( 30 Pi / 16 ) |
| data8 0x3FED906BCF328D46 // cos ( 30 Pi / 16 ) |
| // |
| data8 0xBFC8F8B83C69A60B // sin ( 31 Pi / 16 ) |
| data8 0x3FEF6297CFF75CB0 // cos ( 31 Pi / 16 ) |
| // |
| data8 0x0000000000000000 // sin ( 32 Pi / 16 ) |
| data8 0x3FF0000000000000 // cos ( 32 Pi / 16 ) |
| LOCAL_OBJECT_END(double_sin_cos_beta_k4) |
| |
| .section .text |
| |
| //////////////////////////////////////////////////////// |
| // There are two entry points: sin and cos |
| // If from sin, p8 is true |
| // If from cos, p9 is true |
| |
| GLOBAL_IEEE754_ENTRY(sinf) |
| |
| { .mlx |
| alloc r32 = ar.pfs,1,13,0,0 |
| movl sincosf_GR_sig_inv_pi_by_16 = 0xA2F9836E4E44152A //signd of 16/pi |
| } |
| { .mlx |
| addl sincosf_AD_1 = @ltoff(double_sincosf_pi), gp |
| movl sincosf_GR_rshf_2to61 = 0x47b8000000000000 // 1.1 2^(63+63-2) |
| };; |
| |
| { .mfi |
| ld8 sincosf_AD_1 = [sincosf_AD_1] |
| fnorm.s1 sincosf_NORM_f8 = f8 // Normalize argument |
| cmp.eq p8,p9 = r0, r0 // set p8 (clear p9) for sin |
| } |
| { .mib |
| mov sincosf_GR_exp_2tom61 = 0xffff-61 // exponent of scale 2^-61 |
| mov sincosf_r_sincos = 0x0 // 0 for sin |
| br.cond.sptk _SINCOSF_COMMON // go to common part |
| };; |
| |
| GLOBAL_IEEE754_END(sinf) |
| |
| GLOBAL_IEEE754_ENTRY(cosf) |
| |
| { .mlx |
| alloc r32 = ar.pfs,1,13,0,0 |
| movl sincosf_GR_sig_inv_pi_by_16 = 0xA2F9836E4E44152A //signd of 16/pi |
| } |
| { .mlx |
| addl sincosf_AD_1 = @ltoff(double_sincosf_pi), gp |
| movl sincosf_GR_rshf_2to61 = 0x47b8000000000000 // 1.1 2^(63+63-2) |
| };; |
| |
| { .mfi |
| ld8 sincosf_AD_1 = [sincosf_AD_1] |
| fnorm.s1 sincosf_NORM_f8 = f8 // Normalize argument |
| cmp.eq p9,p8 = r0, r0 // set p9 (clear p8) for cos |
| } |
| { .mib |
| mov sincosf_GR_exp_2tom61 = 0xffff-61 // exponent of scale 2^-61 |
| mov sincosf_r_sincos = 0x8 // 8 for cos |
| nop.b 999 |
| };; |
| |
| //////////////////////////////////////////////////////// |
| // All entry points end up here. |
| // If from sin, sincosf_r_sincos is 0 and p8 is true |
| // If from cos, sincosf_r_sincos is 8 = 2^(k-1) and p9 is true |
| // We add sincosf_r_sincos to N |
| |
| ///////////// Common sin and cos part ////////////////// |
| _SINCOSF_COMMON: |
| |
| // Form two constants we need |
| // 16/pi * 2^-2 * 2^63, scaled by 2^61 since we just loaded the significand |
| // 1.1000...000 * 2^(63+63-2) to right shift int(W) into the low significand |
| // fcmp used to set denormal, and invalid on snans |
| { .mfi |
| setf.sig sincosf_SIG_INV_PI_BY_16_2TO61 = sincosf_GR_sig_inv_pi_by_16 |
| fclass.m p6,p0 = f8, 0xe7 // if x=0,inf,nan |
| mov sincosf_exp_limit = 0x10017 |
| } |
| { .mlx |
| setf.d sincosf_RSHF_2TO61 = sincosf_GR_rshf_2to61 |
| movl sincosf_GR_rshf = 0x43e8000000000000 // 1.1000 2^63 |
| };; // Right shift |
| |
| // Form another constant |
| // 2^-61 for scaling Nfloat |
| // 0x10017 is register_bias + 24. |
| // So if f8 >= 2^24, go to large argument routines |
| { .mmi |
| getf.exp sincosf_r_signexp = f8 |
| setf.exp sincosf_2TOM61 = sincosf_GR_exp_2tom61 |
| addl gr_tmp = -1,r0 // For "inexect" constant create |
| };; |
| |
| // Load the two pieces of pi/16 |
| // Form another constant |
| // 1.1000...000 * 2^63, the right shift constant |
| { .mmb |
| ldfe sincosf_Pi_by_16_1 = [sincosf_AD_1],16 |
| setf.d sincosf_RSHF = sincosf_GR_rshf |
| (p6) br.cond.spnt _SINCOSF_SPECIAL_ARGS |
| };; |
| |
| // Getting argument's exp for "large arguments" filtering |
| { .mmi |
| ldfe sincosf_Pi_by_16_2 = [sincosf_AD_1],16 |
| setf.sig fp_tmp = gr_tmp // constant for inexact set |
| nop.i 999 |
| };; |
| |
| // Polynomial coefficients (Q2, Q1, P2, P1) loading |
| { .mmi |
| ldfpd sincosf_P2,sincosf_Q2 = [sincosf_AD_1],16 |
| nop.m 999 |
| nop.i 999 |
| };; |
| |
| // Select exponent (17 lsb) |
| { .mmi |
| ldfpd sincosf_P1,sincosf_Q1 = [sincosf_AD_1],16 |
| nop.m 999 |
| dep.z sincosf_r_exp = sincosf_r_signexp, 0, 17 |
| };; |
| |
| // p10 is true if we must call routines to handle larger arguments |
| // p10 is true if f8 exp is >= 0x10017 (2^24) |
| { .mfb |
| cmp.ge p10,p0 = sincosf_r_exp,sincosf_exp_limit |
| nop.f 999 |
| (p10) br.cond.spnt _SINCOSF_LARGE_ARGS // Go to "large args" routine |
| };; |
| |
| // sincosf_W = x * sincosf_Inv_Pi_by_16 |
| // Multiply x by scaled 16/pi and add large const to shift integer part of W to |
| // rightmost bits of significand |
| { .mfi |
| nop.m 999 |
| fma.s1 sincosf_W_2TO61_RSH = sincosf_NORM_f8, sincosf_SIG_INV_PI_BY_16_2TO61, sincosf_RSHF_2TO61 |
| nop.i 999 |
| };; |
| |
| // sincosf_NFLOAT = Round_Int_Nearest(sincosf_W) |
| // This is done by scaling back by 2^-61 and subtracting the shift constant |
| { .mfi |
| nop.m 999 |
| fms.s1 sincosf_NFLOAT = sincosf_W_2TO61_RSH,sincosf_2TOM61,sincosf_RSHF |
| nop.i 999 |
| };; |
| |
| // get N = (int)sincosf_int_Nfloat |
| { .mfi |
| getf.sig sincosf_GR_n = sincosf_W_2TO61_RSH // integer N value |
| nop.f 999 |
| nop.i 999 |
| };; |
| |
| // Add 2^(k-1) (which is in sincosf_r_sincos=8) to N |
| // sincosf_r = -sincosf_Nfloat * sincosf_Pi_by_16_1 + x |
| { .mfi |
| add sincosf_GR_n = sincosf_GR_n, sincosf_r_sincos |
| fnma.s1 sincosf_r = sincosf_NFLOAT, sincosf_Pi_by_16_1, sincosf_NORM_f8 |
| nop.i 999 |
| };; |
| |
| // Get M (least k+1 bits of N) |
| { .mmi |
| and sincosf_GR_m = 0x1f,sincosf_GR_n // Put mask 0x1F - |
| nop.m 999 // - select k+1 bits |
| nop.i 999 |
| };; |
| |
| // Add 16*M to address of sin_cos_beta table |
| { .mfi |
| shladd sincosf_AD_2 = sincosf_GR_32m, 4, sincosf_AD_1 |
| (p8) fclass.m.unc p10,p0 = f8,0x0b // If sin denormal input - |
| nop.i 999 |
| };; |
| |
| // Load Sin and Cos table value using obtained index m (sincosf_AD_2) |
| { .mfi |
| ldfd sincosf_Sm = [sincosf_AD_2],8 // Sin value S[m] |
| (p9) fclass.m.unc p11,p0 = f8,0x0b // If cos denormal input - |
| nop.i 999 // - set denormal |
| };; |
| |
| // sincosf_r = sincosf_r -sincosf_Nfloat * sincosf_Pi_by_16_2 |
| { .mfi |
| ldfd sincosf_Cm = [sincosf_AD_2] // Cos table value C[m] |
| fnma.s1 sincosf_r_exact = sincosf_NFLOAT, sincosf_Pi_by_16_2, sincosf_r |
| nop.i 999 |
| } |
| // get rsq = r*r |
| { .mfi |
| nop.m 999 |
| fma.s1 sincosf_rsq = sincosf_r, sincosf_r, f0 // r^2 = r*r |
| nop.i 999 |
| };; |
| |
| { .mfi |
| nop.m 999 |
| fmpy.s0 fp_tmp = fp_tmp, fp_tmp // forces inexact flag |
| nop.i 999 |
| };; |
| |
| // Polynomials calculation |
| // Q = Q2*r^2 + Q1 |
| // P = P2*r^2 + P1 |
| { .mfi |
| nop.m 999 |
| fma.s1 sincosf_Q = sincosf_rsq, sincosf_Q2, sincosf_Q1 |
| nop.i 999 |
| } |
| { .mfi |
| nop.m 999 |
| fma.s1 sincosf_P = sincosf_rsq, sincosf_P2, sincosf_P1 |
| nop.i 999 |
| };; |
| |
| // get rcube and S[m]*r^2 |
| { .mfi |
| nop.m 999 |
| fmpy.s1 sincosf_srsq = sincosf_Sm,sincosf_rsq // r^2*S[m] |
| nop.i 999 |
| } |
| { .mfi |
| nop.m 999 |
| fmpy.s1 sincosf_rcub = sincosf_r_exact, sincosf_rsq |
| nop.i 999 |
| };; |
| |
| // Get final P and Q |
| // Q = Q*S[m]*r^2 + S[m] |
| // P = P*r^3 + r |
| { .mfi |
| nop.m 999 |
| fma.s1 sincosf_Q = sincosf_srsq,sincosf_Q, sincosf_Sm |
| nop.i 999 |
| } |
| { .mfi |
| nop.m 999 |
| fma.s1 sincosf_P = sincosf_rcub,sincosf_P,sincosf_r_exact |
| nop.i 999 |
| };; |
| |
| // If sinf(denormal) - force underflow to be set |
| .pred.rel "mutex",p10,p11 |
| { .mfi |
| nop.m 999 |
| (p10) fmpy.s.s0 fp_tmp = f8,f8 // forces underflow flag |
| nop.i 999 // for denormal sine args |
| } |
| // If cosf(denormal) - force denormal to be set |
| { .mfi |
| nop.m 999 |
| (p11) fma.s.s0 fp_tmp = f8, f1, f8 // forces denormal flag |
| nop.i 999 // for denormal cosine args |
| };; |
| |
| |
| // Final calculation |
| // result = C[m]*P + Q |
| { .mfb |
| nop.m 999 |
| fma.s.s0 f8 = sincosf_Cm, sincosf_P, sincosf_Q |
| br.ret.sptk b0 // Exit for common path |
| };; |
| |
| ////////// x = 0/Inf/NaN path ////////////////// |
| _SINCOSF_SPECIAL_ARGS: |
| .pred.rel "mutex",p8,p9 |
| // sinf(+/-0) = +/-0 |
| // sinf(Inf) = NaN |
| // sinf(NaN) = NaN |
| { .mfi |
| nop.m 999 |
| (p8) fma.s.s0 f8 = f8, f0, f0 // sinf(+/-0,NaN,Inf) |
| nop.i 999 |
| } |
| // cosf(+/-0) = 1.0 |
| // cosf(Inf) = NaN |
| // cosf(NaN) = NaN |
| { .mfb |
| nop.m 999 |
| (p9) fma.s.s0 f8 = f8, f0, f1 // cosf(+/-0,NaN,Inf) |
| br.ret.sptk b0 // Exit for x = 0/Inf/NaN path |
| };; |
| |
| GLOBAL_IEEE754_END(cosf) |
| |
| //////////// x >= 2^24 - large arguments routine call //////////// |
| LOCAL_LIBM_ENTRY(__libm_callout_sincosf) |
| _SINCOSF_LARGE_ARGS: |
| .prologue |
| { .mfi |
| mov sincosf_GR_all_ones = -1 // 0xffffffff |
| nop.f 999 |
| .save ar.pfs,GR_SAVE_PFS |
| mov GR_SAVE_PFS = ar.pfs |
| } |
| ;; |
| |
| { .mfi |
| mov GR_SAVE_GP = gp |
| nop.f 999 |
| .save b0, GR_SAVE_B0 |
| mov GR_SAVE_B0 = b0 |
| } |
| .body |
| |
| { .mbb |
| setf.sig sincosf_save_tmp = sincosf_GR_all_ones // inexact set |
| nop.b 999 |
| (p8) br.call.sptk.many b0 = __libm_sin_large# // sinf(large_X) |
| };; |
| |
| { .mbb |
| cmp.ne p9,p0 = sincosf_r_sincos, r0 // set p9 if cos |
| nop.b 999 |
| (p9) br.call.sptk.many b0 = __libm_cos_large# // cosf(large_X) |
| };; |
| |
| { .mfi |
| mov gp = GR_SAVE_GP |
| fma.s.s0 f8 = f8, f1, f0 // Round result to single |
| mov b0 = GR_SAVE_B0 |
| } |
| { .mfi // force inexact set |
| nop.m 999 |
| fmpy.s0 sincosf_save_tmp = sincosf_save_tmp, sincosf_save_tmp |
| nop.i 999 |
| };; |
| |
| { .mib |
| nop.m 999 |
| mov ar.pfs = GR_SAVE_PFS |
| br.ret.sptk b0 // Exit for large arguments routine call |
| };; |
| LOCAL_LIBM_END(__libm_callout_sincosf) |
| |
| .type __libm_sin_large#, @function |
| .global __libm_sin_large# |
| .type __libm_cos_large#, @function |
| .global __libm_cos_large# |
| |
